# Full text of "Mathematical And Physical Papers - Iii"

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```ON THE MOTION OF PENDULUMS.                           31
which agrees with the result deduced directly from the ordinary equations of hydrodynamics*.
18. Let us now form the expression for the resultant of the pressures of the fluid on the several elements of the surface of the sphere. Let Pr be the normal, and Te the tangential, component of the pressure at any point in the direction of a plane drawn perpendicular to the radius vector. The formulae (4), (5) are general, and therefore we may replace #, y in these formulae by Co, y'y where xy y' are measured in any two rectangular directions we please. Let the plane of x' y' pass through the axis of x and the radius vector, and let the axis of oc be inclined to that of x at an angle ^, which after differentiation is made equal to 0. Then Pv Ts will become Pr, Te, respectively. We have
u = R cos (6 - *) - © sin (0 - *) , v = R sin (6 - ty + @ cos (6 - \$•),
and when 0 = \$•
d      d      d       d
_             _=__           _^
dx ~~ dr '   dy     rdd     r }  ~d% ~~~ dr ' whence